Problem: Find an explicit formula for the arithmetic sequence $-2,-14,-26,-38,...$. Note: the first term should be $\textit{d(1)}$. $d(n)=$
Solution: The general explicit formula for arithmetic sequences is ${a_1}+{d}(n-1)$, where ${a_1}$ is the first term and $ d$ is the common difference. The first term is ${-2}$ and the common difference is ${-12}$. ${-12\,\curvearrowright}$ ${-12\,\curvearrowright}$ ${-12\,\curvearrowright}$ ${-2},$ $-14,$ $-26,$ $-38,...$ This is the explicit formula for the arithmetic sequence $-2,-14,-26,-38,...$. $d(n)={-2}{-12}(n-1)$ Note that this solution strategy results in this formula, however an equally correct solution can be written in other equivalent forms as well.